Lie algebras hiding in multi-linear operations

Speaker: José São João ，Université de Strasbourg         

Inviter: Vladimir Dotsenko

Title: Lie algebras hiding in multi-linear operations

Language: English

Time & Venue: 2026.10.09    16:00-17:00    南楼N913

Abstract: The derivative of a linear species can be viewed as a categorification of the derivative of formal power series. The derivative of an operad carries the structure of a twisted associative algebra and a right module of the operad. In this talk we will show that the derivative of topological operads with units give rise to connected cocommutative twisted Hopf algebras. By a twisted version of the Milnor–Moore theorem, such twisted Hopf algebras are the universal enveloping algebras of twisted Lie algebras. Using this we present the derivative of the d-Gerstenhaber operad as the universal envelope of a central extension of a twisted Lie algebra.